Dispersive instrument for measurement of particle size distributions

ABSTRACT

A method for measurement of the size distribution of particles suspended in a gas or in a liquid. The particle suspension is illuminated by a collimated beam of substantially white light. Part of the light scattered by the particles is collected by a lens and is passed through a slit placed in the focal plane of the lens. The light transmitted by the slit is made to pass through a dispersive element which causes spectral decomposition of the processed light in a direction perpendicular to the slit. A spatial filter is placed in the exit plane of the dispersive element; the transmittance of this filter is a function of position on the filter. The light transmitted by the filter is measured by a photodetector. The photodetector output is measured as different spatial filters are switched in place. A computer, microprocessor, or analog device acts on the measured values and produces the particle size distribution as an output. The data reduction algorithm consists of a linear transformation of the measured data vector, followed by the construction of a linear combination of basis functions for the size distribution. One of the spatial filters has uniform transmittance for the purpose of background light subtraction, and to provide a bias in order to allow effectively indefinite filter transmittance functions.

CROSS REFERENCE TO COPENDING APPLICATIONS

This is a continuation in part of applicant's copending United Statespatent application Ser. No. 919,281, filed June 26, 1978, now U.S. Pat.No. 4,245,909 entitled, OPTICAL INSTRUMENT FOR MEASUREMENT OF PARTICLESIZE DISTRIBUTIONS, and also of applicant's copending United Statespatent application Ser. No. 113,673, filed Jan 21, 1980, entitledMULTIPLE WAVELENGTH INSTRUMENT FOR MEASUREMENT OF PARTICLE SIZEDISTRIBUTIONS, the latter also being a continuation of the former.

This invention was made during the course of work performed under acontract with the Office of Naval Research. The invention pertains tothe rapid measurement of the size distribution of particles suspended ina gas or in a liquid. For simplicity the discussion in the presentsection is made to refer to the case of water drops suspended in air. Inmost of the known instruments which are presently available formeasurement of drop size distributions, sample air is moved through asmall highly illuminated volume of space, and light scattered by theindividual drops, as they move in a single file through this volume, ismeasured by a photodetector. The drop size is determined from theintensity of the electric pulse out of the photodetector. This methodsuffers from a number of deficiencies, notably the edge effect, thevelocity effect and counter swamping. The edge effect arises becausedrops which pass through the scattering volume near the edge of theilluminating beam are illuminated less and therefore scatter less light.This causes the instrument to undersize the drop. The velocity effectarises in airborne applications, where the cloud drops move rapidlythrough the scattering volume. The resulting short detector pulseduration requires somewhat different electronics parameters than thoseused for terrestrial laboratory work, where the drop velocity is small.As a consequence, laboratory calibration of the instrument unless it isdone in a windtunnel, is of limited utility for airborne measurements.Counter swamping may occur when drop size distributions are measured indense clouds aboard a fast flying aircraft.

The measurement method comprised in the present invention suffers fromnone of the deficiencies discussed. Instead of counting and sizingindividual scattering events, the instrument looks at a sizeable volumeof cloud (from about one liter to several cubic meters) and it processesthe light scattered from all drops in this volume collectively. Thismakes it possible to measure drop size distributions in clouds, fogs, orin laboratory cloud chambers in situ, without disturbing the cloud.Furthermore, it becomes possible to perform bulk measurements, in whichaverage drop size distributions in a large volume are determinedrapidly.

In practice, the light scattered by the multitude of individualparticles adds incoherently. In the case of spherical particles, eachparticle scatters light in its characteristic Mie intensity pattern;these Mie patterns superimpose and give rise to a scattered lightintensity which is a certain function of scattering angle. It is theobject of the present invention to provide a means for determining theparticle size distribution from this scattered light function.

Under circumstances often encountered, the conversion from the scatteredlight function to the particle size distribution constitutes anill-conditioned data reduction problem, which results in low instrumentaccuracy. It is a further object of the present invention to circumventthis problem.

The measurement of the scattered light function may be done by means ofan array of photodetectors, as in the apparatus of Malvern Instrument,Ltd., of Malvern Worcestershire, England. This requires thephotodetectors to be small solid state devices, such as photodiodes, andthis restricts the detectivity of the instrument such that onlyrelatively dense particle suspensions can be measured accurately. Usingphotomultiplier tubes instead of photodiodes would result in a muchincreased instrument sensitivity, but use of any array ofphotomultiplier tubes would be prohibitive in cost and size. Therefore,there is merit in a method which requires only a single photodetectorfor the measurement of light scattered by the particles. For thisphotodetector, a photomultiplier tube can then be used.

It is a further object of the present invention to determine theparticle size distribution by using a single photodetector for themeasurement of the light scattered by the particles.

There are several situations in which it is desirable to utilizescattering angles near 180°, i.e., near backscattering. Such anarrangement makes it possible to have the light source and detector inthe same general location, and yet measure particle size distributionsin a large volume or at rather large distances from the apparatus. It isa further object of the present invention to provide a method fordetermining particle size distributions which can be used with nearbackscattered light.

Often, there is undesirable background light in the form of daylight, orfrom light sources extraneous to the instrument. In cloud chamber work,the illuminated cloud drops inside the chamber scatter light in alldirections; some of this light is reflected by or scattered off thechamber walls, and this results in undesirable background light whichenters the instrument. It is a further object of the present inventionto provide means to effectively subtract background light in theinstrument process.

It is yet another object of the present invention to provide a means ofmeasuring particle size distributions in real time.

By way of summary, the objects of the invention are achieved by passinga collimated beam of white polarized light through the particlesuspension and by collecting part of the light scattered by theparticles located in a portion of the illuminating beam by aphotodetector, after the light has passed through a lens and through adispersive element, followed by a spatial filter placed in the exitplane of the dispersive element. Different spatial filters are broughtinto position behind the lens in quick succession, and the sequence ofmeasured photodetector outputs is acted upon by a linear transformation,followed by the formation of a linear combination of basis functions forthe particle size distribution, executed by a computer, microprocessor,or an analog device.

The invention will be fully understood from the following detaileddescription and the accompanying drawings, in which:

FIG. 1 shows schematically an instrument in which a disc is used formounting and switching a plurality of spatial filters;

FIG. 2 shows schematically a modified instrument employing nearbackscattering, and a film strip for switching a plurality of spatialfilters;

FIGS. 3-7 are plan views of transparencies bearing patterns which formspatial filters transmittance functions;

FIG. 8 shows the distribution of the perpendicularly polarized intensityof light scattered by water drops as a function of the scatteringparameter and the scattering angle, illustrating the occurence ofsecondary correlation peaks; and

FIG. 9 shows an arrangement of the invention in which two lenses and aprism are used to make up the dispersive element, and in which a disc isused for mounting and switching of a plurality of spatial filters.

Referring now to FIG. 1, a light source 11 produces a collimated ornearly collimated beam 12 of nearly-monochromatic polarized light, whichilluminates the particle suspension. A lens or lens system 13 processeslight scattered by the particles located in the intersection 12b of thebeam 12 and the cone 14, the latter constituting the field of view of anoptical configuration consisting of lens 13 and an image window 15,located in the focal plane 16 of lens 13.

In this specification, the term "focal plane" is defined as the planewhich sharply images objects at infinity.

A polarizing element 17 is placed in the path of scattered light,preferably but not necessarily between the lens 13 and image window 15.A perfect lens 13 would map incoming light rays located inside cone 14onto points in image window 15. Therefore, part of the light scatteredby an angle θ by all particles in the volume at intersection 12b isimaged onto a curve in window 15. As a consequence for spherical andmonodispersed particles, the light intensity in image window 15 will bedistributed according to a Mie intensity pattern.

A set of (N+1) spatial filters 18 is mounted on a disc 19 in plane 16.Arrangements are made such that, in time, different spatial filters areswitched into the position of window 15.

An alternate embodiment of the switching concept consists of a filmstrip19a, the frames of which are the individual spatial filters. Thefilmstrip is moved past the window in step-wise motionpicture fashion.The filmstrip (FIG. 2) can be looped, without beginning or end, ifpreferred.

There is the option of chopping the beam 12 of light by a chopper 22,and using synchronous detection in a manner which will be evident tothose skilled in the art.

There is the further option of having either disc or filmstrip movecontinuously, and to flash the light source 11 synchronously with thefilter position. A gated amplifier or integrator can then be used in thesignal processing.

Each spatial filter consists of a transparency, the transmittance ofwhich is a function of location on the transparency. Behind the imagewindow 15 and the spatial filter 18 there is a photodetector 20, whichis usually a photomultiplier tube. With the i^(th) spatial filter inplace, the signal from the photodetector 20, usually after amplificationand integration, (possibly gated), is measured and serves as input s_(i)for a computer 21. In the present context, the computer 21 may be acomputer, a microprocessor, or an analog device, such as a CCD or CTD.There are N+1 different spatial filters on the disc 19, and hence, thereare N+1 signals s_(i). The computer 21 is programmed or arranged such asto execute a linear transformation of the data sequence s_(i), i=0,1,-N,by means of a matrix T_(ij), which is present in the computer, orembodied in an analog device, in a manner as will be evident to thoseskilled in the art. The result of this linear transformation is thesequence ##EQU1## j=1,-n. As a further action of the computer, the sum##EQU2## is computed, where the n_(j) (a) are N basis functions for theparticle size distribution function, a being the particle radius, orsome other particle size characterizing number. The function n(a) is theparticle size distribution which is the object of the measurement. Itmay be displayed, printed, or used as input for further calculations ina manner evident to those skilled in the art. The number b_(o) is notused in the particle size distribution calculation (2), since things arearranged such that b_(o) is a measure of the background light, and suchthat the b_(j), j=1,-N, are not influenced by the background light.Essential to this arrangement is the use of one spatial filter, say withj=0, which has uniform transmittance.

The action of the filters may be understood as follows. Suppose that thecloud consists of drops of a uniform size. If for that case the filter18 in the image window 15 would be replaced by a screen, the lightprocessed by the apparatus would illuminate this screen with a nonuniform intensity, showing light and dark bands, which are called a Miepattern. The Mie pattern depends on the scattering angle range in thefield of view of the cone 14, and it also depends on the size and therefractive index of the scattering cloud drops. If now different filtersare switched into place, maximum light would get passed by a filterwhich has a transmittance pattern which precisely matches the MIEpattern of the incoming light. In this manner, the Mie pattern of thelight coming into the window 15 is recognized, and the drop size isinferred. For a cloud with a mixture of drop sizes, the algorithymdiscussed unravels the separate contributions by the Mie patternsbelonging to the different drop sizes to the total light intensitydistribution in the window. It is possible to use filter transmittancedistributions other than Mie patterns belonging to single drop sizes, bytaking linear combinations of such Mie patterns for different sizes.

In order to enable those skilled in the art to construct the propertransmittance functions for the spatial filters 18, the followingdiscussion is presented, in which square integrable functions areconsidered as vectors in a Hilbert space H. Let n denote the vector ofthe particle size distribution n(a), and let v denote the vector of thelight intensity distribution of the scattered light incident on theimage window 15. Since in practical cases the light scattered by theindividual particles adds incoherently, one has

    v=Mn,                                                      (3)

where M is a linear operator on H, which may be thought of as aninfinite dimensional matrix. If M is non singular, one has

    n=M.sup.-1 v,                                              (4)

where M⁻¹ is the inverse of M. In practice, measurement of v containsnoise Δv, which results in a noise part

    Δn=M.sup.-1 Δv                                 (5)

in the measured particle size distribution. From (4) and (5) one has##EQU3## where ∥ denotes the Euclidean norm (see, for instance, W.Schmeidle "Linear Operators in Hilbert Space", Academic Press, New York,1965, pages 10 and 13). Therefore, the inverse map (4) brings about asignal to noise ratio degradation ##EQU4## where the maximum is takenover non-negative functions n, and the minimum is taken over functionsΔn which have no definiteness restriction. In (6), the vectors n and Δnover which the maximum and minimum are taken may be restricted to asubspace S of H. Then, Δ depends on the subspace S, and, of course, onthe scattering angle interval comprized by the field of view cone 14. Ifβ₀ is an acceptable value for the degradation of the inverse map (4), asubspace S of H is called good if β≦β₀. The data reduction methodoutlined amounts to approximating particle size distributions as vectorsin a good subspace G. The utility of this procedure depends on whetherin practice particle distribution and their differences have negligiblecomponents in the orthogonal compliment B of G. Calculations have shownthat for waterdrops in air, and for scattering angle ranges away fromnear-forward or near backward directions, the subspace B containsvectors Δn which can occur in practice as the difference between broadpolydispersed drop size distributions. This is because in the Mieintensity pattern for monodispersed waterdrops in air the maxima andminima in the region away from the near forward and near backwarddirections shift very rapidly with changing scattering parameter α=2πa/λ(a is the drop radius, and λ is the light wavelength), whereas thedistance between consecutive maxima varies slowly with α. Hence, if oneadds the Mie patterns of two drops of slightly different sizes, themaxima and minima fill in, thereby diminishing the norm of the accomponent of v. It follows that an instrument designed for a scatteringangle range away from the near-forward or near-backward directions isonly suitable to measure rather monodisperse drop size distributions.For accurate measurement of broad polydisperse drop size distributionone must use near-forward or near backward scattering as in FIG. 2. Thisis because for varying α the scattering intensity versus scatteringangle θ always has a maximum at θ=0, and either a maximum or a minimumat θ=180°. Therefore, the "phase" of the Mie "waves" is locked in atθ=0°, and at θ=180° (up to a flip of π), so that, near these angles, themaxima and minima do not change position so rapidly as function of α.Furthermore, comput studies have shown that the near-backscatter rangeis more suitable for the accurate measurement of broad polydisperseddrop size distributions, if Gaussians with a relative standard deviationof about 10% are used as basis functions, in a manner described below.Let the N linearly independent basis functions n_(i), i=1,-N, belong tothe good subspace G. We approximate the particle size distribution as alinear combination ##EQU5## With

    v.sub.i =Mn.sub.i                                          (8)

one has ##EQU6## A solution for b_(i) may be obtained by forming thescalar products (correlations) ##EQU7## where

    C.sub.ij =v.sub.i ·v.sub.j.                       (11)

One then has ##EQU8## where C_(ij) ⁻¹ is the inverse of C_(ij). Theparticle size distribution is found from ##EQU9## The correlationv·v_(j) is implemented in the present invention by passing the scatteredlight through lens 13 and through the j^(th) spatial filter 18 withtransmittance V_(j) in focal plane 16 of lens 13. The light incident onthe filter has the intensity distribution v. The total light intensitytransmitted by the filter is v·v_(j). C_(ij) ⁻¹ is essentially theinstrument matrix T_(ij) of (1); further discussion clarifying the roleof i=0 or j=0 follows.

Since the basis functions n_(j) lie in the good subspace G, they can bechosen such that the matrix is far from singular, and the matrixmultiplication (13) does not give rise to a large degradation of signalto noise ratio. (12) written in the form ##EQU10## shows that the lineartransformation can be absorbed in the optical process, by taking spatialfilters with transmittance functions ##EQU11## Resulting negativetransmittance can be embodied in practice by using a bias to raise allfilter transmittances to nonnegative values, and by adding an (N+1) stfilter (J=0) with a uniform transmittance. This filter can also be usedto achieve subtraction of background light, by considering the uniformfunction n_(o) as the density of a "dummy" scattering object, whichgives a scattering function v_(o) equal to the background lightcontribution to v. Including the dummy scatterer in (7) gives ##EQU12##and extending the range of j in (12) gives ##EQU13## where now, C_(ij)⁻¹ is the inverse of the N+1 dimensional matrix C_(ij). The bi,i=1,-N,of (16) are not influenced by the background light. The inclusion of thelinear transformation in the optical process, and the biasing of thefilter transmittances to non-negative values may be done as follows.Inclusion of j=0 in (14) gives ##EQU14## Let C_(i) be a positive numbersuch that none of the functions ##EQU15## attains negative valuesanywhere on the window 15. Then, with a_(i) =max g_(i), the functionsg_(i),i=1,-N, are implementable as transmittance functions of thefilters i=1,-N, (17) may be written

    b.sub.i =a.sub.i v·g.sub.i -c.sub.i (v·v.sub.o), i=1,-N. (19)

If s_(i) is the photodetector signal with the ith filter in position.(19) may be written

    b.sub.i =a.sub.i s.sub.i -c.sub.i s.sub.o, i=1,-N.         (20)

Hence, this embodiment gives a shorter computer calculation of thecoefficients b_(i) of expansion of the particle size distribution η(a)in terms of the basis functions n_(i) (a), i=1,-N.

It will be evident to those skilled in the art how to apply thisprocedure to the case in which the background light illuminates window15 in a non-uniform manner, and a 0th filter with an appropriatenon-uniform transmittance is used for the implementation of indefinitefilter transmittances. The description above has been given in terms ofwater drops in air. It applies as well to other spherically symmetricparticles, suspended in a gas or a liquid except that certain ratios ofrefractive index of the particles and the suspending medium may favornear forward scattering rather than near backscattering. In such cases,the scattering angle range must be appropriately adjusted, but themethod of measurement and date reduction remains the same. The methodalso applies to the case of nonspherically symmetric particles suspendedin a gas or liquid, possibly with some degradation of performance of theinstrument. The particles may be biological cells, bacteria, or otherbiological organisms, and the invention may be used to determine theconcentrations of the various species of cells, bacteria, organisms, orparticles which are present in a sample. The particles may be suspendedon a transparent slide which is illuminated by the light beam, insteadof being suspended by a gas or a liquid in the bulk.

There are various options concerning the polarization of the beam 12,and the polarizing element 17, as follows. The instrument will work withan unpolarized light source 11, and without the polarizing element 17.In fact, this is the preferred polarization mode for very near forwardscattering or very near backscattering, i.e., where the intensities ofthe scattered light in both polarized directions are substantially thesame. For scattering angles not very close to 0° or 180°, an improvementin instrument performance is achieved by using a light source 11 whichis polarized. (E direction) perpendicular to the plane P through theilluminating beam axis and the optical axis of the lens. The use of apolarizing element 17 is then optional; if used, the polarizationdirection should be perpendicular to the plane P. As an alternative, anunpolarized light source 11 can be used, together with a polarizationelement 17, polarized perpendicular to the plane P. As a furtheralternative, the light source 11 may be polarized in the direction of P,and there is then again the option of using a polarizing element 17; ifused, the element 17 should be polarized in the direction of P. As afurther alternative, an unpolarized light source may be used, withelement 17 polarized in the direction of P.

A modified instrument which is particularly suitable for use in cloudsof fog is shown schematically in FIG. 2. In this case, nearbackscattering is used, making it possible to have light source 11 anddetector unit close together while sampling a substantial volume ofcloud or fog. The element numbers are the same as in FIG. 1, with theexception of the embodiment of the set of filters, which now is in theform of a filmstrip 19a looped and therefore without end. It isimportant that either the illuminating light intensity in beam 12 isvery nearly the same from frame to frame exposure of the filmstrip, orelse that the variation of this light intensity is measured accurately.It will be evident to those skilled in the art how to achieve thisobjective, if necessary by the use of an auxiliary photodetector whichmeasures the illuminating light intensity.

FIGS. 3-7 show examples of negatives of transmittance functions forspatial filters for use in FIG. 1 with scattering angle near 90°. Thesefunctions have been generated by a computer-driven plotter, from acalculation of Mie intensities for water drops in air. In these plots,the dot density along vertical lines is proportional to the averagefilter transmittance along vertical lines. In this particular example,the average scattering angle is 90°, and the coarse-grained averagefilter transmittance is approximately constant along vertical lines. Foraverage scattering angles different from 90°, the filter transmittanceis constant along curves which are conical sections of constantscattering angle θ.

Another method for the construction of the filters consists of making apicture in the form of a slide, of a semi-transparent sheet assembly,which is illuminated from the opposite side of the camera, where thesheet assembly consists of strips of semi-transparent material such aspaper, but together in layers in such a manner as to produce an assemblywith the desired transmittance pattern.

Yet another method for the construction of the filters consists ofproducing a cloud with uniform drop size, or with a certain desired dropsize distribution, and using a camera instead of the assembly 13, 18, 19and 20, in such a manner that the camera lens is identical to the lens13, and is placed in the position of lens 13 and such that the camerafilm window coincides with the image window 15. Using the properexposure time, the picture produced in this manner, in the form of aslide, will have the proper transmittance pattern. A preferred methodfor the construction of the filters consists of controlling a cameraorientation by means of two computer-driven angular positioners, andilluminating the camera lens with a fixed collimated light beam, whichpasses through a computer-controlled shutter. Alternatively, theintensity of the light beam may be modulated by the computer.

When a polarizing element is placed in the path of the scattered light,it may be placed on either side of the lens, preferably ahead of thespatial filter.

Chopping or flashing the light source is useful but not essential. Asteady light source can be used. However, significant advantages areobtained by providing light intermittently, for example improvement inthe signal to noise ratio, discrimination against background light, anddiscrimination against dc output voltage drift of the amplifiers behindthe photodetector.

The accuracy of instruments of the type discussed above may be furtherimproved by using multiple-wavelength light and by including adispersive element in the detector optics, in a manner as describedbelow.

Eq. (8) may be written

    v.sub.i (θ)=   da M(θ,α)n.sub.i (a),     (21)

where a is the particle radius, n_(i) (a) is the particle sizedistribution for the ith basis function, a, and a₂ are respectively thesmallest and largest particle radii in the size distribution n_(i) (a),M(θ,α) is the differential scattering cross section, and α is thescattering parameter defined before,

    α=2πa/λ,                                   (22)

where λ is the wavelength of the monochromatic light used. With (21),Eq. (11) may be written

    C.sub.ij =   dθ   da da'M(θα)M(θ,α')n.sub.i (a)n.sub.j (a'),(23)

where θ₁ and θ₂ are respectively the smallest and largest scatteringangles for the light processed by the instrument optics, and

    α'=2πa'/λ.                                 (24)

Eq. (23) may be rewritten as

    C.sub.ij =      αaαa'n.sub.i (a)g(a,a')n.sub.j (a'), (25)

where

    g(a,a')=   dθ M(θα)M(θ,α')   (26)

is seen to serve as a metric in the Hilbert space of square integrableparticle size distributions η(a); in fact, (25) may be seen as thescalar product n_(i) ·n_(j) in that Hilbert space, using the metric(26).

The data reduction algorithm (13) involves the inverse C_(ij) ⁻¹ of thematrix C_(ij). Therefore, the degradation of the signal to noise ratioin the data reduction will depend on the condition number of the matrixC_(ij) (defined as the ratio of maximum to minimum absolute values ofthe eigenvalues). In turn, this condition number is influenced by thecondition number of the metric g(a,a'). Eq. (26) shows that this metricis just the correlation (over the interval θ₁,θ₂) of the differentialscattering cross sections M(θ,α) and M(θ,α'). This correlation has apeak for α'=α, but there exist secondary correlation peaks as well forcertain values of α and α'. This may be seen from FIG. 8, which showsthe differential cross section M(θ,α) for the perpendicularly polarizedcomponent of light scattered by water drops. In this figure the symbol Ais used for the scattering parameter, instead of α. The Mie functionM(θ,A) is plotted in the form of contour lines as function of thescattering paramter A and the scattering angle θ; the numerical valuesfor the contours shown are ##EQU16## where i₁ is the perpendicularlypolarized scattered light intensity. In this case, one has θ₁ =145° andθ₂ =152°. FIG. 8 may be seen as a topograhic map of terrain withmountains, lakes, valleys, ridges, and canyons. It may be seen that theridge-like mountain at about A=11.4 is quite similar to the ridge-likemountain at about A=16.3; this similarity extends at least over aninterval ΔA≈1 to the right. It follows that the correlation (26) has asecondary peak for α in the neighborhood of 11.5 and α-α'≈4.8. Suchsecondary correlation peaks adversely affect the condition number of themetric g(a,a'), and thereby diminish the instrument accuracy.

This problem may be alleviated to a considerable extent by using lightwith a plurality of different wavelengths such that the opticalprocessing involves the sum or integral of correlations at differentwavelengths λ.

For that case, the sequence of Eqs. (8) to (13) becomes ##EQU17##similar modifications, amounting to replacing the scalar product • bythe "color" scalar product • , apply to the remaining equations, (14) to(20). Eq. (10') shows that the color scalar product • is simply theintegral, over the wavelengths from λ, to λ₂, of the ordinary scalarproduct • in Hilbert space. If for the transmittance function forwavelength λ of the spatial filter j one chooses the function v_(j) (λ),then the correlation v • v_(j) occuring in (13') is implemented by thespatial filter action. For the multiple-wavelength case one has, insteadof Eqs. (21) to (26), ##EQU18## The relief from strong secondarycorrelation peaks provided by the wavelength integral in (26') is nowevident: for a and a'≠a such that there is a strong correlation in onewavelength, there is usually weak correlation in other wavelengths;hence, in the wavelength integral (26'), the secondary correlation peaksare diminished.

The implementation of the multiple-wavelength scheme may be accomplishedas follows. Referring to FIG. 9, a light source 400 produces acollimated or nearby collimated beam 401 of substantially white light,which illuminates the particle suspension. The beam 401 has an axis401a. A lens or lens system 402 processes light scattered by theparticles located in the intersection 403 of the beam 401 and the cone404, the latter constituting the field of view of an opticalconfiguration consisting of lens 402, and a slit 405 in an opaque screen406, located in the focal plane of lens 402. The slit 405 is orientedsuch that it is substantially parallel to the scattering plane for aprocessed scattered light ray which runs along the optical axis 402a ofthe lens 402; this scattering plane is substantially parallel to theoptical axis 402a and the beam axis 401a. A polarizing element 407 isplaced in the path of the scattered light, preferably but notnecessarily between the lens 402 and the slit 405.

The scattered light which is transmitted by the slit 405 is made to passthrough a dispersive element consisting of a lens 408, a prism or set ofprisms 409, and a lens 410, in such a manner that the slit 405 is in thefocal plane of lens 408, and focussed spectral decomposition of theprocessed light is obtained in the exit plane 411, which is the focalplane of lens 410. The prism orientation is such that the prismgenerators are parallel to the slit 405.

A set of spatial filters 412 is mounted on a disc 413 in plane 411.Arrangements are made such that in time, different spatial filters areswitched in the position of window 414, located in plane 411.

An alternate embodiment of the switching concept consists of afilmstrip, the frames of which are the individual spatial filters. Thefilmstrip is moved past the window 414, in step-wise motion-picturefashion. The filmstrip can be looped, without beginning or end, ifpreferred.

The spatial filters 412 of FIG. 9 are black and white transparencieswith certain spatial transmittance functions of the coordinates x and yin the plane 411.

There is the option of chopping the beam 401, and using synchronousdetection in a manner which will be evident to those skilled in the art;the chopping may be done mechanically or by switching of the lightsource 400.

There is the further option of having either disc or filmstrip movecontinuously, and to flash the light source 400 synchronously with thefilter position. A gated amplifier or integrator can then be used in thesignal processing.

Behind the image window 414 and the spatial filter 412 there is aphotodetector 415, which is usually a photomultiplier tube. With the ithspatial filter in place, the signal from the photodetector 415, usuallyafter amplification and integration, (possibly gated), is measured andserves as input s_(i) for a computer 416, which may be a computer, amicroprocessor, or an analog device, such as a CCD, or CTD. There areN+1 different spatial filters on the disc 413, and hence, there are N+1signals s_(i). The computer 416 is programmed such as to execute thealgorithm (13'), where the matrix C_(ij) ⁻¹ is the inverse of the matrixC_(ij) given by (11'). Background subtraction may be achieved bycolor-generalizing Eq. (16), and biasing the filter transmittances tonon-negative values may be achieved by color-generalizing Eqs. (17),(18), (19), and (20), in a manner which will be evident to those skilledin the art. The considerations concerning polarization, as discussedabove for the monochromatic instrument, apply without change to themultiple-wavelength instrument. The same comment applies to theconsideration pertaining to the illuminating light intensities for thedifferent frames or spatial filters.

The dispersive element, shown in FIG. 9 to consist of the lens 408, theprism or prisms 409, and the lens 410, may be implemented differently bymeans involving a grating or hologram in a manner evident to thoseskilled in the art.

All the methods for construction of the spatial filters which arediscussed above for the single wavelength case may be used for themultiple-wavelength instrument as well. The preferred method for theconstruction of the spatial filters consists again of controlling acamera orientation by means of two computer-driven angular positioners,and by illuminating the camera lens with a fixed collimated light beam,which either passes through a computer-controlled shutter, or else, hasan intensity modulated by the computer.

This invention is not to be limited by the embodiments shown in thedrawings and described in the description, which are given by way ofexample and not of limitation, but only in accordance with the scope ofthe appended claims.

What is claimed is:
 1. A method for measurement of the size distributionof particles suspended in a gas or a liquid, comprising:passing into theparticle suspension an illuminating beam comprising a substantiallycollimated beam of substantially white light; with a lens collectingpart of the light scattered by the particles; passing the collectedlight through a slit in an opaque screen located in the focal plane ofsaid lens; passing the light transmitted by said slit through adispersive element such as to produce, in the exit plane of thedispersive element, a spectral decomposition in a directionperpendicular to said slit, and such that a monochromatic point sourcein said slit produces a sharp image in said exit plane; sequentiallyplacing the members of a set of spatial filters in an image windowlocated in said exit plane; collecting the light transmitted by each ofsaid spatial filters sequentially by a photodetector to produce a signalsubstantially proportional to light transmitted by respective filters;acting on the resulting photodetector signal sequence by a lineartransformation; and using the resulting data sequence a coefficients ina linear combination of basis functions to yield the particle sizedistribution.
 2. A method according to claim 1 in which the spatialfilters have a non-uniform transmittance which at any point P of thefilters is a function of λ and θ, where λ is the wavelength at P and θis the scattering angle of rays that pass through P.
 3. A methodaccording to claim 1 in which one of the filters of the set has auniform transmittance.
 4. A method according to claim 3 in which thesaid acting by a linear transformation step comprises an opticalprocess, and is followed by a step of subtracting the scaledphotodetector signal for the uniform filter from the scaled signals forthe non-uniform filters, followed by the step of using using theresulting data sequence as coefficients in a linear combination of basisfunctions.
 5. A method according to claim 3 in which said uniformtransmittance filter is used for subtraction of background light.
 6. Amethod according to claim 1 in which said set of spatial filters movescontinuously, and the light source is flashed when a member of the setof spatial filters is aligned with said image window.
 7. A methodaccording to claim 6 in which synchronous detection is used to processthe photodetector signal.
 8. A method according to claim 1 in which apolarizing element is placed in the path of the said scattered light. 9.A method according to claim 8 in which spatial filters have anon-uniform transmittance which at any point P of the filter is afunction of λ and θ, where λ is the wavelength at P and θ is thescattering angle of rays that pass through P.
 10. A method according toclaim 8 in which one of the filters of the set of spatial filters has auniform transmittance.
 11. A method according to claim 10 in which thesaid acting by a linear transformation step comprises an opticalprocess, and is followed by a step of subtracting the scaledphotodetector signal for the uniform filter from the scaled signals forthe non-uniform filters, followed by the step of using the resultingdate sequence as coefficients in a linear combination of basisfunctions.
 12. A method according to claim 10 in which said uniformtransmittance filter is used for subtraction of background light.
 13. Amethod according to claim 8 in which said set of spatial filters movescontinuously, and the light source is flashed when a member of the setof spatial filters is aligned with said image window.
 14. A methodaccording to claim 13 in which synchronous detection is used to processthe photodetector signal.
 15. A method according to claim 8 in which alight chopper is placed in the illuminating beam.
 16. A method accordingto claim 15 in which synchronous detection is used to process thephotodetector signal.
 17. A method according to claim 1 in which a lightchopper is placed in the illuminating beam.
 18. A method according toclaim 17 in which synchronous detection is used to process thephotodetector signal.
 19. A method according to claim 1 in which saidsubstantially collimated beam is polarized.
 20. A method according toclaim 19 in which the spatial filters have a non-uniform transmittancewhich at any point P of the filter is a function of λ and θ, where λ isthe wavelength and θ is the scattering angle of rays that pass throughP.
 21. A method according to claim 19 in which one of the filters of theset has a uniform transmittance.
 22. A method according to claim 21 inwhich the said acting by a linear transformation step comprises anoptical process, and is followed by a step of subtracting the scaledphotodetector signal for the uniform filter from the scaled signals forthe non-uniform filters, followed the step of using the resulting datasequence as coefficients in a linear combination of basis functions. 23.A method according to claim 21 in which said uniform transmittancefilter is used for subtraction of background light.
 24. A methodaccording to claim 19 in which said set of spatial filters movescontinuously, and the light source is flashed when a member of the setof spatial filters is aligned with said image window.
 25. A methodaccording to claim 24 in which synchronous detection is used to processthe photodetector signal.
 26. A method according to claim 19 in which alight chopper is placed in the illuminating beam.
 27. A method accordingto claim 26 in which synchronous detection is used to process thephotodetector signal.
 28. Apparatus for measurement of the sizedistribution of particles suspended in a gas or liquid comprising:asource of substantially collimated beam of substantially white light,which illuminates the particle suspension; a lens for collecting part ofthe light scattered by the particles; an opaque screen with a slit, saidscreen being located in the focal plane of said lens; a dispersiveelement through which the light transmitted by said slit is passed, andwhich in its exit plane produces a spectrally decomposed image of saidslit, the spectral decomposition encompassing the dimension of the exitplane perpendicular to the slit; a set comprising a plurality of spatialfilters; means to present filters of said set sequentially in an imagewindow located in said exit plane of the dispersive element; aphotodetector to produce a sequence of signals each of which issubstantially proportional to light transmitted by a respective filter;means for acting on the resulting photodetector signal sequence by alinear transformation; and means for using the resulting data sequenceas coefficients in a linear combination of basis functions to yield theparticle size distribution.
 29. Apparatus according to claim 28 in whichthe filters are mounted on a rotatable disc.
 30. Apparatus according toclaim 28 in which the filters are comprised of a film strip. 31.Apparatus according to claim 28 in which the filters comprisetransparencies which have a non-uniform transmittance which at any pointP of the filter is a function of λ and θ, where λ is the wavelength andθ is the scattering angle of rays that pass through P.
 32. Apparatusaccording to claim 28 in which polarizing means is placed in the path ofthe beam provided by said source.
 33. Apparatus according to claim 28 inwhich chopper means, synchronized with the spatial filter set,intermittently impedes the passage of light into the suspension. 34.Apparatus according to claim 33 in which means for synchronous detectionis used to process the photodetector signal.
 35. Apparatus according toclaim 28 in which means is provided for flashing said light sourceintermittently.
 36. Apparatus according to claim 35 in which means forsynchronous detection is used for the photodetector signal. 37.Apparatus according to claim 28 in which polarizing means is placed onthe axis of said lens, ahead of said filters.
 38. Apparatus formeasurement of the size distribution of particles suspended in a gas orliquid comprising:a source of substantially collimated beam ofsubstantially white light, which illuminates the particle suspension; alens for collecting part of the light scattered by the particles; anopaque screen with a slit, said screen being located in the focal planeof said lens; a dispersive element consisting of an entrance lens, a setof η prisms, η≧1, and an exit lens, such that the said opaque screen isin the focal plane of the entrance lens, the light transmitted by theslit and the entrance lens traverses the said set of prisms as well asthe exit lens, and the prism generators are substantially parallel tothe said slit; an image window located in the rear focal plane of saidexit lens; a set comprising a plurality of spatial filters; means topresent filters of said set sequentially in said image window; aphotodetector to produce a sequence of signals each of which issubstantially proportional to light transmitted by a respective filter;means for acting on the resulting photodetector signal sequence by alinear transformation; and means for using the resulting data sequenceas coefficients in a linear combination of basis functions to yield theparticle size distribution.
 39. Apparatus according to claim 38 in whichthe filters are mounted on a rotatable disc.
 40. Apparatus according toclaim 38 in which the filters comprise a filmstrip.
 41. Apparatusaccording to claim 38 in which the filters comprise transparencies whichhave a non-uniform transmittance, which at any point P of the filters isa function of λ and θ, where λ is the wavelength and θ is the scatteringangle of rays that pass through P.
 42. Apparatus according to claim 38in which polarizing means is placed in the path of the beam provided bysaid source.
 43. Apparatus according to claim 38 in which chopper means,synchronized with the spatial filter set, intermittently impedes thepassage of light into the suspension.
 44. Apparatus according to claim43 in which means for synchronous detection is used to process thephotomultiplier signal.
 45. Apparatus according to claim 38 in whichmeans is provided for flashing said light source intermittently. 46.Apparatus according to claim 45 in which means for synchronous detectionis used to process the photodetector signal.
 47. Apparatus according toclaim 38 in which polarizing means is placed on the axis of said lens,ahead of said filters.